Question

In general, the standard deviation of a randomly chosen individual security will have lower standard deviation of a large index (like S&P 500)

A. False because individual securities are riskier.
B. False because individual securities have lower idiosyncratic risk.
C. True because indices contain large number of securities.
D. True because the risk of securities in the index adds up.

Answer 1

The standard deviation of a randomly chosen individual security will have a lower standard deviation than a large index like the S&P 500 because indices contain a large number of securities, which helps to reduce the overall risk of the index through diversification.

Step-by-step explanation:

The correct answer is C. True because indices contain a large number of securities.

When we calculate the standard deviation of a large index like the S&P 500, the risk of individual securities in the index is diversified or spread out across many different stocks. This diversification helps to reduce the overall risk of the index. However, when we calculate the standard deviation of a randomly chosen individual security, it may have higher risk because it is not diversified like the index.

For example, if you invest in a single stock and that stock performs poorly, your entire investment will be affected. However, if you invest in an index like the S&P 500, the poor performance of one stock will have less impact on your overall investment because it is spread out across many stocks.